#9326 ⟨a, b | ab=a, baaa=bba⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative non-commutative monoid
- Element b has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ b = a and a ⋅ 1 = a, however b ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
a3 ⋅ a = a2 and a ⋅ a = a2, however a3 ≠ a
- Reduction order:
- Left-to-right recursive path with deg(a) = 0; deg(b) = 1
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ab=a,baaa=bba a/b - -
aaaa=aa
ab=a
bba=baaa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
4 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 25546 | ⟨a, b | ab=a, baaab=bba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25554 | ⟨a, b | ab=a, baaba=bba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25570 | ⟨a, b | ab=a, babaa=bba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25878 | ⟨a, b | ab=a, bbab=baaa⟩ | φ(a) = a, φ(b) = b |